2.6 Multivariate CAPM - The Arbitrage Pricing Theory

The capital asset pricing model may be the standard-bearer today, but no one regards it as the final word in finance. Some day a new model will probably come along that works better. It may be a new twist on the basic CAPM, or it may be something new altogether.

Most of the theories that are used today are some iteration or extension of the CAPM. However, in 1976 MIT Professor Stephen Ross proposed a new model that bears no family resemblance. What follows is a brief sketch of the basic theory.

For full detail, it would be worth reading Ross’s pioneering article, “The Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory 13: 341-60 (December 1976) (JET prior to 1993 is only available in print through the Z. Smith Reynolds/Chatham offsite collection).

The CAPM, despite its flaws, has led economists to wonder whether the relationship between risk and return is captured by other measures of risk, besides ß. Perhaps there are risks besides volatility, which is all that ß measures. Perhaps other proxies (such as company size) can be used to measure risk. For example, studies indicate that larger companies have higher returns than smaller companies with the same price volatility. See Barr Rosenberg, Kenneth Reid & Ronald Lanstein, Persuasive Evidence of Market Inefficiency, J. Portfolio Mgmt. 9 (Spr. 1985) (finding ratio of equity's book value to market price correlated to average returns for U.S. stocks). Size may be a surrogate for greater liquidity -- and investors will pay to reduce this risk factor.

From this insight, economists have constructed an Arbitrage Pricing Theory that relates multiple risk factors to determine expected returns. Under this model, an asset's expected return is calculated according to its sensitivity to each risk factor. For example, a portfolio's returns might be seen as depending both on systematic risk and liquidity. APT predicts that the market capital line will actually be a two-dimensional plane in which various combinations of risk and liquidity produce different returns. (For models with multiple risk factors, returns can be derived from a multi-dimensional hyperplane.)

APT assumes, like CAPM, that as an asset's price departs from the capital market plane, investors will engage in arbitrage transactions (buy low, sell high) until the asset's price is pushed back towards the plane.

So, you ask, which risk factors determine the capital market hyperplane? Well, the APT is currently agnostic. Maybe future research will show which risk factors matter, and how much they influence expected returns. At least four measurable factors seem relevant:

• level of industrial activity (economic risk)
• spread between short- and long-term interest rates (inflation risk)
• the spread between the yields of low- and high-risk corporate bonds (default risk)
• bid-ask spread (liquidity risk).